Problem: $g(x)=9x-2$ $h(x)=3x^2+2x$ Write $h(g(x))$ as an expression in terms of $x$. $h(g(x))=$
Let's write $g(x)$ as the input to function $h$. $h({g(x)})=3({g(x)})^2+2({g(x)})$ Since $g(x)=9x-2$, this becomes: $\begin{aligned} h({g(x)})&=3({9x-2})^2+2({9x-2})\\ \\ &=3(81x^2-36x+4)+18x-4\\ \\ &=243x^2-108x+12+18x-4\\ \\ &=243x^2-90x+8 \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $h(g(x))=243x^2-90x+8$